Kaz
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 Jan 10 comment Do people wearing glasses have different field of view than those who don't? Glasses: yes; contacts: no. Jul 9 comment Special relativity: where does this naive calculation go wrong? And, brilliant, the distance 5.196 is precisely two (contracted) ship lengths: $2\times 2.6\ \text m$ which is because the light pulse is half a $c$ faster than the ship. Just like a point moving at 100 km/h needs two car lengths of road to pass 50 km/h car. Jul 9 comment Special relativity: where does this naive calculation go wrong? Okay, this makes sense now. The time of exit of the pulse is at a different location (front of ship versus back), and so it appears further delayed, and the time blows up to 17.3 nanoseconds, not 11.5. Jul 9 comment Special relativity: where does this naive calculation go wrong? Ah, I think this must be due to signs being treated in other than the expected way in the coordinate transform. This result matches what we would expect if the light pulse were entering from the front and leaving from the back, traversing less than 2.6 meters. Jul 9 comment Special relativity: where does this naive calculation go wrong? The thing is, how can the distance traveled by the light be seen as shorter than the contracted length of the ship's cabin of 2.60 meters. That's one of the counter-intuitive facts here. A pulse of light enters the back of the ship, which is 2.6 meters long and moving forward at $c/2$; how can that light leave the ship's front only 1.73 meters down the path? Jul 9 comment Special relativity: where does this naive calculation go wrong? I don't understand the results intuitively. $\Delta t'$ works out to be only 5.77 nanoseconds. And $\Delta x'$ works out to 1.73 m, the familiar number from earlier calculations which now has a different interpretation. So in fact, the time between the beam entering/leaving events is faster in the standing reference frame and it so happens that the total distance traveled by the beam of light is 1.73 m. Jul 9 comment Special relativity: where does this naive calculation go wrong? ... so, I think it's the $-v\Delta x/c^2$ term in the time dilation that is at the root of this: we must account for the change in position when judging the time dilation. If that is the case, I find my intuition weakening here. But wait, $\Delta x$ is in the $S$ frame, I see? So in other words, aha, because the two events are at different positions in the $S$ frame (rear of ship versus front), we have to take that into account. The simple form of the time dilation only applies to one place, like a single clock in the spaceship. Jul 9 comment Special relativity: where does this naive calculation go wrong? Thanks. I, by the way, had tried the $v\Delta t$ term in the length calculation, suspecting that the error may be that the two events are sampled at different times. In my example, all that did was produce the 2.6 meter condensed length: $\Delta x$ is the 4.33 m, and $v\Delta t$ is the 1.73 m movement. I.e. the more general form with the $v\Delta t$ term simply lets us confirm that the ship is 2.6 meters long even though we sample the position of its front and rear at different times: the beam crossings separated by 11.54 ns. Mar 8 comment Can you put a magnetic ball into a hollow magnetic sphere? @ChrisGerig A sphere is an abstract geometric surface; it consists of points. Jul 18 comment If there were fundamental forces weaker than gravity, would we know about it? @Void The arrow clearly points outside of Slovakia, somewhere in Poland. Moreover, the entire rectangle around the "landscape" is understood to be the "swamp", not only some small area near the tip of the arrow. Apr 8 comment Why isn't jumping from a high altitude fatal? First paragraph lacks a relative clause "After seeing ..... (stuff in parentheses) ___ WHAT?" Jan 20 comment Why do shadows from the sun join each other when near enough? Diffraction. I learned about this in the fifth grade. Nov 24 comment Why are radiators always placed under windows? @PPG Yes, but your desk has space underneath for the air to flow and probably some clearance from its edge to the legs. If there is a radiator or baseboard heater, under the window, it's easier to put a desk there than, say, a dresser cabinet (even one that is short enough not to extend past the windowsill). Cabinets will have a small cutaway for baseboard trim; that's about it. Nov 19 comment Why don't metals bond when touched together? @deed02392 Note that large flat objects pressed together are also hard to separate simply due to atmospheric pressure. The space between them is a void, and air has to rush in when you separate them. Early in the separation, the crevice through which air can get in is small. Nov 19 comment Why don't metals bond when touched together? @jcw An electric current can break through the oxidation layers. This is called fritting. Though not an instance of welding, it explains why high voltage electrical contacts don't have to be maintained much. Even a pretty tarnished appliance plug, for instance, will work fine. But, say, small-signal connectors (e.g. audio) will not perform well if they are not clean and polished. (It's good for high voltage connectors to be in good condition too, so that fritting doesn't have to be relied on so much. A high initial contact resistance that has to be broken down could briefly generate heat.) Nov 15 comment How to measure speed of a ceiling fan? Hopefully, paramedics won't have to be called. Oct 19 comment What's inside a proton? @DavidZ Because due to surpassing some hotness threshold or whatever, it has appeared in the stackexchange-network-wide list of hot questions, which creates a positive feedback loop of upvoting. Oct 19 comment What's inside a proton? Note that "empty space" is just a philosophical abstraction. Ultimately, space is the name we give to that handy utility which prevents everything from occupying the same spot. How much space is between two particles depends on how fat you consider them to be: where is the boundary between what is in the particle and what is outside. This is complicated by the boundary being fuzzy: just a sort of density function, which is not even time-invariant. Sep 29 comment Why does burning things make them black? @fzlogic And elemental carbon can be a hard, transparent crystal: diamond. Aug 28 comment Why do chimneys have these spiral “wings”? Is this vortex shedding why cables whine in the wind? It seems not unlike what happens in some blown-hole woodwind instruments, too.